Lets draw a picture of our points:
since triangles are similar the following ratios must be preserved:
[tex]\begin{gathered} \text{ratioX}=\frac{\text{xred}}{\text{xgreen}} \\ \text{ratioY=}\frac{\text{yred}}{ygreen} \end{gathered}[/tex]
where these values come from the following picture:
for the first x red-ratio, we have
[tex]\text{ratioX}=\frac{8-6}{3-2}=\frac{2}{1}=2[/tex]
for green-ratio, we have
[tex]\text{ratioY}=\frac{7-1}{3-(-2)}=\frac{6}{5}[/tex]
Then, by applying these results, the ratios from point S=(x,y) to point N=(7,5) must be
[tex]\begin{gathered} \frac{x}{7}=2 \\ \frac{y}{5}=\frac{6}{5} \end{gathered}[/tex]
From the first relation, we get
[tex]x=7\times2=14[/tex]
and from the second relation, we have
[tex]y=5\times\frac{6}{5}=6[/tex]
then, the searched point S has coordinates S=( 14,6)
